Here’s a nice little animated diagram from Fathom Information Design that compares the two polar opposites of transit mapping using Boston’s MBTA rail network as an example. Click through to play around with it, and see the benefits and drawbacks of the two approaches. It’s also super fun to watch the map morph between the two styles.

In real life, most transit maps fall somewhere between these two extremes: very few use such a strict topological grid, and completely geographically accurate maps are also very rarely used for this purpose – even the New York subway map has a certain level of simplification and abstraction.